Description

This package implements methods for methods for conducting subgroup analyses and estimating the impact of implementing the optimal individualized treatment strategy in the population.

Installation

To install the package via devtools, use

devtools::install_github("alexluedtke12/sg")

Example

We now present an example on a sample of size n=1000. The SuperLearner library is small so that the example does not take long to run -- in practice, we recommend using a larger SuperLearner library.

library(sg)

sim.data = function(nn){
	W = data.frame(W1=rnorm(nn),W2=rnorm(nn),W3=rnorm(nn),W4=rnorm(nn))
	A = rbinom(nn,1,1/2)
	Y = rbinom(nn,1,Qbar(A,W))
	return(list(W=W,A=A,Y=Y))
}

SL.library = c('SL.mean','SL.glm')

n = 1000
Qbar = function(a,w){plogis(-1 + 2*a*w$W1)} # function(a,w){plogis(a*(w$W1>0)*w$W1)}

# data to run methods on
dat = sim.data(n)
W = dat$W
A = dat$A
Y = dat$Y

# data to evaluate true parameter values
n.mc = 2e4
dat = sim.data(n.mc)
W.mc = dat$W
A.mc = dat$A
Y.mc = dat$Y
blip.mc = Qbar(1,W.mc)-Qbar(0,W.mc)

Below each example, we also print the true impact of implementing the rule, i.e. the quantity that sg.cvtmle is estimating.

# Contrast optimal treatment strategy against treating with probability 1/2
sg.cvtmle(W,A,Y,SL.library=SL.library,txs=c(0,1),baseline.probs=c(1/2,1/2),CATE.SL.library=SL.library,sig.trunc=0.001,family=binomial(),kappa=1,num.SL.rep=2,num.est.rep=2,lib.ests=TRUE,verbose=FALSE)

## $est
## SuperLearner      SL.mean       SL.glm 
##   0.13394596   0.06408995   0.13412034 
## 
## $ci
##                      lb         ub
## SuperLearner 0.10831312 0.15957880
## SL.mean      0.03743888 0.09074101
## SL.glm       0.10849102 0.15974966
## 
## $est.mat
##              SuperLearner    SL.mean    SL.glm
## Repetition 1    0.1357762 0.06413537 0.1357762
## Repetition 2    0.1321157 0.06404452 0.1324645

# truth
mean(Qbar(1,W.mc)*((blip.mc>0)-1/2) + Qbar(0,W.mc)*((blip.mc<=0)-1/2))

## [1] 0.1242482

# Contrast optimal treatment strategy against treating everyone with tx 0
sg.cvtmle(W,A,Y,SL.library=SL.library,txs=c(0,1),baseline.probs=c(1,0),CATE.SL.library=SL.library,sig.trunc=0.001,family=binomial(),kappa=1,num.SL.rep=2,num.est.rep=2,lib.ests=TRUE,verbose=FALSE)

## $est
## SuperLearner      SL.mean       SL.glm 
##    0.1991847    0.1279397    0.1990086 
## 
## $ci
##                      lb        ub
## SuperLearner 0.15403755 0.2443319
## SL.mean      0.07459551 0.1812839
## SL.glm       0.15386105 0.2441562
## 
## $est.mat
##              SuperLearner   SL.mean    SL.glm
## Repetition 1    0.1994651 0.1273042 0.1991129
## Repetition 2    0.1989044 0.1285752 0.1989044

# truth
mean((blip.mc)*(blip.mc>=0))

## [1] 0.1655005

# Resource constraint: at most 25% can be treated. Contrast against treating everyone with tx 0
sg.cvtmle(W,A,Y,SL.library=SL.library,txs=c(0,1),baseline.probs=c(1,0),CATE.SL.library=SL.library,sig.trunc=0.001,family=binomial(),kappa=0.25,num.SL.rep=2,num.est.rep=2,lib.ests=TRUE,verbose=FALSE)

## $est
## SuperLearner      SL.mean       SL.glm 
##    0.1863364    0.1280433    0.1863364 
## 
## $ci
##                      lb        ub
## SuperLearner 0.13782888 0.2348439
## SL.mean      0.07467649 0.1814101
## SL.glm       0.13782509 0.2348477
## 
## $est.mat
##              SuperLearner   SL.mean    SL.glm
## Repetition 1    0.1874353 0.1293991 0.1874353
## Repetition 2    0.1852375 0.1266875 0.1852375

# truth
mean((blip.mc)*(blip.mc>=max(quantile(blip.mc,1-0.25),0)))

## [1] 0.1290834